Archaeological Data
The Ainu people are descended primarily from the Jōmon people and secondarily from the Yayoi. Modern Japanese people are descended primarily from the Yayoi, secondarily from the Jōmon, and tertiarily from ethnic Koreans. There is still debate whether the Yayoi emigrated to the Japanese Archipelago from Mumun period Korea or from the Yuyue State in Eastern Zhou period China. In either case, neither group's religious culture was as similar to modern Shinto as Jōmon & Ainu animism is.
Keep in mind that 氏神{うじがみ} are tied to specific locations which would mean that the emigrants (Yayoi/Japanese) either established new sacred places in Japan or the natives (Jōmon/Ainu) had already established certain areas as sacred.
Linguistic Data
The kanji 神
predates the Yayoi by several hundred years, showing up in oracle bone script.
[かみ] often appears in compounds as /kamu/ (modern /kaɴ/), indicating that /kami/ is a bound or fused form deriving from */kamu.i/. Note that this final i may be the Old Japanese emphatic nominative particle い (i), likely cognate with Korean nominative particle 이 (i). Such fusion has occurred in other Japanese terms, such as 目 (me, “eye”, from ma + i) or 酒 (sake, “saké, liquor”, from saka + i).
~Wiktionary
Even with the combination of the above evidence we can't definitively say that かみ
originated as カムイ
, but it is the most likely scenario given the available data.
Please comment if I've missed anything above.
/te/
, 目{ま} + い ⇒/me/
, 木{こ} + い ⇒/ki/
, and for 神{かむ} + い ⇒/kami/
. Frellesvig himself mentions the possibility of い fusion in his paper "Old Japanese Particles" (search for "particle i").